[tex]\frac{10}{n+7} * C^{n+5}_{n +7}=\frac{10}{n+7} *\frac{(n+7)!}{(n+5)!*((n+7)-(n+5))!} =\frac{10}{n+7} *\frac{(n+7)!}{(n+5)!*2!} =\frac{10}{n+7} *\frac{1*2*3*...*(n+5)*(n+6)*(n+7)}{1*2*3*...*(n+5)*2}=\frac{10}{n+7} *\frac{(n+6)*(n+7)}{2}=\frac{10*(n+6)*(n+7)}{(n+7)*2} =5*(n+6)=5n+30[/tex]
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[tex]\frac{10}{n+7} * C^{n+5}_{n +7}=\frac{10}{n+7} *\frac{(n+7)!}{(n+5)!*((n+7)-(n+5))!} =\frac{10}{n+7} *\frac{(n+7)!}{(n+5)!*2!} =\frac{10}{n+7} *\frac{1*2*3*...*(n+5)*(n+6)*(n+7)}{1*2*3*...*(n+5)*2}=\frac{10}{n+7} *\frac{(n+6)*(n+7)}{2}=\frac{10*(n+6)*(n+7)}{(n+7)*2} =5*(n+6)=5n+30[/tex]